The answer to this depends on the specific facts of the case, but generally speaking if one executor acts alone without the knowledge or consent of the other executor, and makes a mess of it, the executor who caused the problem is the only one responsible.
If they are both at fault, then usually both will be equally responsible for the loss. However, one fact that can make a big difference is the identity of the co-executor. For example, if one of the co-executors is a lawyer, he or she might end up being held the only one responsible, even though both co-executors participated in the actions. This is because the lawyer has specialized knowledge and training that should have an impact on how that lawyer behaves as an executor.
Trust companies are, just like lawyers, held to a higher standard than individual executors because of the experience and training of the trust company's staff. This can mean that if a trust company is a co-executor with an individual and both executors participate in a transaction that causes a loss to the estate, the trust company might be held solely responsible.
Executors and co-executors can be held liable for the actions of others if they hire people to help them with an estate. Frequently executors will hire lawyers, accountants, realtors, appraisers, investment advisors and others to carry out specific jobs within the estate administration. Sometimes the person hired may make a mistake that leads to a preventable loss on the estate. Is the executor responsible for that?
As long as the person hired does ONLY the work that is within his or her specialty, any loss due to an error is not the executor's responsibility; it's the hired person's responsibility. But if that executor asks the hired person to do anything that is not their specialty (for example, a lawyer completing a tax return or a realtor giving investment advice) and there's a mistake, that is considered the fault of the executor.
The rules are somewhat complicated when it comes to figuring out who is to blame for something. This is why executors and co-executors are told the rules of how they are expected to act when they take on the job.